Kinematical higher-twist corrections in γ*→M1M2γ : Charged meson production

Generalized distribution amplitudes (GDAs) of mesons can be probed by the reactions <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:msub><a:mi>M</a:mi><a:mn>1</a:mn></a:msub><a:msub><a:mi>M</a:mi><a:mn>2</a:mn></a:msub><a:mi>γ</a:mi></a:math>, which are accessible at electron-positron colliders such as BESIII and Belle II. After discussing the neutral meson production case in our previous paper, we discuss here the complementary case of the charged meson (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msup><d:mi>M</d:mi><d:mo>+</d:mo></d:msup><d:msup><d:mi>M</d:mi><d:mo>−</d:mo></d:msup></d:math>) production, where one can extract the complete information on GDAs from the interference of the amplitudes of the two competing processes where the photon is emitted either in the initial or in the final state. Considering the importance of the charged meson production, we present a complete expression for the interference term of the cross section, which is experimentally accessible thanks to its charge conjugation specific property. We adopt two types of models for leading-twist <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>π</f:mi><f:mi>π</f:mi></f:math> GDAs to estimate the size of the interference term in the process <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msup><h:mi>e</h:mi><h:mo>−</h:mo></h:msup><h:msup><h:mi>e</h:mi><h:mo>+</h:mo></h:msup><h:mo stretchy="false">→</h:mo><h:msup><h:mi>π</h:mi><h:mo>+</h:mo></h:msup><h:msup><h:mi>π</h:mi><h:mo>−</h:mo></h:msup><h:mi>γ</h:mi></h:math> numerically, namely, a model extracted from previous experimental results on <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>γ</k:mi><k:mo>*</k:mo></k:msup><k:mi>γ</k:mi><k:mo stretchy="false">→</k:mo><k:msup><k:mi>π</k:mi><k:mn>0</k:mn></k:msup><k:msup><k:mi>π</k:mi><k:mn>0</k:mn></k:msup></k:math> at Belle and the asymptotic form predicted by QCD evolution equations. We include in the calculation the kinematical power suppressed (sometimes called kinematical higher-twist) corrections up to <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mn>1</n:mn><n:mo>/</n:mo><n:msup><n:mi>Q</n:mi><n:mn>2</n:mn></n:msup></n:math> for the helicity amplitudes. Both models of GDAs indicate that the kinematical corrections are not negligible for the interference term of the cross section measured at BESIII, thus it is necessary to include them if we try to extract the GDAs precisely. On the other side, the kinematical corrections are very tiny for the measurements at Belle II, and the leading twist-two formula of the interference term will be good enough to describe the charge conjugation odd part of the differential cross section.